Problem $1$

Suppose it is the start of year $2008.$ You have $$100,000$ to invest and decide to invest in a combina$-$

tion of a riskless asset $(f),$ a stock index fund $(S)$ and a long$-$term bond fund $(B),$ with the following

properties:

The correlation of the returns on the long$-$term bond fund and the stock index fund is equal to $0\mathrm{.}3.$

a$)$ If you only consider the risky assets, what is the global minimum variance portfolio? What

is the global minimum variance portfolio if you also consider the risk$-$free asset?